The city’s’ Bravest climbed their way to a $10,000 finish yesterday in the 24th Annual Empire State Building Run-Up, while two veteran race champs pulled off thrilling three-peats.

Some 150 runners took part in the race, clambering up the 1,576 steps to the 86th floor, 1,050 feet above ground.

The race, sponsored by Fleet Bank and the New York Road Runners Club, attracted two five-man teams from the Fire and Police departments. They squared off for bragging rights and the $10,000 first prize in the first ever “Fleet Challenge.”

“It’s fun to razz them after the event,” said firefighter Larry Parker, 37, whose team won the $10,000 for the Fire Safety Education Fund. The New York Police Department Widows and Orphans Fund received $5,000.